The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A041008 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A041008

Numerators of continued fraction convergents to sqrt(7).
(history; published version)

#42 by Harvey P. Dale at Fri Jul 23 16:58:02 EDT 2021

STATUS

editing

approved

#41 by Harvey P. Dale at Fri Jul 23 16:57:59 EDT 2021

MATHEMATICA

LinearRecurrence[{0, 0, 0, 16, 0, 0, 0, -1}, {2, 3, 5, 8, 37, 45, 82, 127}, 40] (* Harvey P. Dale, Jul 23 2021 *)

STATUS

approved

editing

#40 by N. J. A. Sloane at Mon Aug 24 23:14:06 EDT 2020

STATUS

editing

approved

#39 by N. J. A. Sloane at Mon Aug 24 23:14:04 EDT 2020

PROG

(PARI) A41008A041008=contfracpnqn(c=contfrac(sqrt(7)), #c)[1, ][^-1] \\ Discard possibly incorrect last element. NB: a(n)=A41008A041008[n+1]! For more terms use:

A041008(n)={n<#A41008A041008|| A41008A041008=extend(A41008, A041008, [4, 16; 8, -1], n\.8); A41008A041008[n+1]}

STATUS

approved

editing

#38 by Joerg Arndt at Sat Nov 02 11:26:51 EDT 2019

STATUS

reviewed

approved

#37 by Michel Marcus at Sat Nov 02 10:47:14 EDT 2019

STATUS

proposed

reviewed

#36 by M. F. Hasler at Sat Nov 02 10:32:35 EDT 2019

STATUS

editing

proposed

Discussion

Sat Nov 02

10:47

Michel Marcus: sorry then

#35 by M. F. Hasler at Sat Nov 02 10:32:17 EDT 2019

CROSSREFS

Analog for other sqrt(m): A001333 (m=2), A002531 (m=3), A001077 (m=5), A041006 (m=6), A041010 (m=8), A005667 (m=10), A041014 (m=11), A041016 (m=12), ..., A042934 (m=999), A042936 (m=1000).

STATUS

proposed

editing

Discussion

Sat Nov 02

10:32

M. F. Hasler: is it better understandable this way ?

#34 by Michel Marcus at Sat Nov 02 04:03:26 EDT 2019

STATUS

editing

proposed

Discussion

Sat Nov 02

10:31

M. F. Hasler: not better, ... represents m=12 ... m=999 !

#33 by Michel Marcus at Sat Nov 02 04:03:20 EDT 2019

LINKS

C. Elsner, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL14/Elsner/elsner9.html">Series of Error Terms for Rational Approximations of Irrational Numbers </a>, J. Int. Seq. 14 (2011) # 11.1.4.

C. Elsner, M. Stein, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL14/Elsner2/elsner10.html">On Error Sum Functions Formed by Convergents of Real Numbers</a>, J. Int. Seq. 14 (2011) # 11.8.6.

CROSSREFS

Analog for other sqrt(m): A001333 (m=2), A002531 (m=3), A001077 (m=5), A041006 (m=6), A041010 (m=8), A005667 (m=10), A041014 (m=11), ..., A042936 (m=1000).

STATUS

proposed

editing

Discussion

Sat Nov 02

04:03

Michel Marcus: ok ?